JEDDAH, Saudi Arabia—A group of some of the world’s biggest crude producers said they would keep a tight grip on output for the rest of the year, and perhaps into next, capitalizing on the success so far of a risky bet they made 18 months ago to throttle back and lift oil prices.

Senior officials from OPEC, Russia and other big producers gathered here Friday said they were happy with a deal they put in place to 2016 to limit production and erase what was then a large glut of stored oil sloshing around the world.